## Monday, November 01, 2004

### Photons have mass?

So the question that was raised initially was how does the classic physics equation of F=MA apply if M is the mass of a photon, which has zero mass. The response was that a photon has zero mass at rest but has mass in motion giving it “momentum”. The definition of momentum follows:

Momentum, also linear momentum, in physics, fundamental quantity characterizing the motion of any object (see Mechanics). It is the product of the mass of a moving particle multiplied by its linear velocity. Momentum is a vector quantity, which means that it has both magnitude and direction. The total momentum of a system made up of a collection of objects is the vector sum of all the individual objects' momenta. For an isolated system, total momentum remains unchanged over time; this is called conservation of momentum. For example, when a batter hits a baseball, the momentum of the bat just before it strikes the ball plus the momentum of the pitched baseball is equal to the momentum of the bat after it strikes the ball plus the momentum of the hit baseball. As another example, imagine a beaver jumping off a stationary log that is floating on water. Before the beaver jumps, the log and the beaver are not moving, so the total momentum is zero. Upon jumping, the beaver acquires forward momentum, and at the same time the log moves in the other direction with an equal and opposite momentum; the total momentum of the beaver plus the log remains at zero.

Conservation of momentum is one of the most important and universal of the conservation laws of physics; it holds true even in situations where modern theories
of physics apply. In particular, conservation of momentum is valid in quantum mechanics (see Quantum Theory), which describes atomic and nuclear phenomena, and in relativistic mechanics, which must be used when systems move with velocities that approach the speed of light (see Relativity).
According to Newton's second law of motion—named after the English astronomer, mathematician, and physicist Sir Isaac Newton—the force acting on a body in motion must be equal to its time rate of change of momentum. Another way of stating Newton's second law is that the impulse—that is, the product of the force multiplied by the time over which it acts on a body—equals the change of momentum of the body.

With that understanding of Momentum we turn to the Physicist’s explanation which follows – read carefully.

While light does indeed have no rest mass, it has momentum. It also has a relativistic mass, but this is concept is rather outdated. The term mass in modern terminology 'mass' refers to the invariant mass, which is zero for photons. This invariant mass is defined by

m = sqrt(E^2/c^4 - p^2/c^2)

where E is energy, c the speed of light, and p the momentum. In the case of light, p = E/c, so the mass is zero. But you already know that. The important thing is that light has a non-zero momentum despite having zero mass.

In an atom, there are electrons orbiting a nucleus in discrete energy levels. This just means that there are only certain distances from the nucleus an electron can be. When an electron becomes excited due to something transferring energy to it, the electron goes to a higher energy level, where it will stay there for an extremely short time. When the electron falls back to its original energy level, it emits a photon, and sometimes the photon is in the visible range of the spectrum. If you search for "Bohr atom" or "spectra" online, you should find some nice diagrams that illustrate this.

As for a light bulb, well, that's filled with an inert gas, usually argon. The bulb also contains a (usually) tungsten wire that carries the electric current. In a solid conductor, the current is generated by the movement of free electrons through the wire. The electrons bump into atoms along their way, and excite the bound electrons, causing them to go to a higher energy level. When the electrons return to their ground state, a photon is emitted. Metals tend to emit in the infa-red, which is invisible to humans. However, if heated to a high enough temperature, the metal will emit in the visible range of the EM spectrum.

This explanation seems very glib to me and smacks of the usual scientific game of naming things without actually understanding them. The fundamental problem here – in fact there are several fundamental problems. Consider that light has no mass at rest – because light is (presumably) never at rest. However, light does in fact have mass and this has been demonstrated (Einstein) because light bends when passed through a strong gravitational field. If a “photon” is emitted when an electron takes on energy that moves it to a higher shell and then returns to its natural state it gives up a photon – the photon has energy but no mass – except that it does have mass. In fact the electron has mass, better still the universe is essentially all energy and that energy has mass. This leaves with these questions:

• If the electron takes on energy and changes its state why doesn’t it take on Mass?

• If the electron gives up a photon when returning to its natural state where does the photon’s mass come from?

• If the electron never took on any mass when moving to the higher state and never lost any mass when returning and the energy level remained the same throughout then where did the photon’s mass come from? Why doesn’t the law of conservation of energy apply?

• If the free electron bumps into bound electrons why isn’t there any loss or gain of energy?

It seems to me that when two objects collide there is an exchange of kinetic energy but with electrons this doesn’t seem to apply – why? If that exchange is the photon and all it receives is energy then that energy has mass – but where did it come from since the electrons neither gained nor lost mass.

Obviously I am not a physicist and my questions might (probably do) parade my ignorance, but this whole explanation of the mass of a photon doesn’t ring true. I think – intuitively I admit – that photons have mass and that light can be captured and weapon-ized (Star Trek’s Photon Torpedoes). I think this is an illustration of how science is structured to fit the thinking of the scientists without any real explanation of what or why.